Here's the conditions on the TPE-SYD Business Save fare below.
You can also check through the booking engine by either clicking the "Fare Family" Name, in this case, the "Business Save" fare or by adding different stopovers during the multi city option in the booking engine on cx.com I tested both, and a SYD-HKG stopover is priced 3 times more than that free TPE-HKG stopover!

Anyhow, here it is.

#Routing
Taiwan to Australia
Travel Class
Business
Rebooking
Free of Charge
Cancellation Fee
Before departure: TWD2400
After departure: TWD2400
Mileage Accrual
You can accrue Asia Miles on this fare
Upgrade with Miles
Permitted
Pre-book Your seat
Permitted
Stopover
Stopover Hong Kong:
1 Stop(s) permitted. On the inbound not permitted. On the outbound free of charge.